796 research outputs found
Parallelization of Markov chain generation and its application to the multicanonical method
We develop a simple algorithm to parallelize generation processes of Markov
chains. In this algorithm, multiple Markov chains are generated in parallel and
jointed together to make a longer Markov chain. The joints between the
constituent Markov chains are processed using the detailed balance. We apply
the parallelization algorithm to multicanonical calculations of the
two-dimensional Ising model and demonstrate accurate estimation of
multicanonical weights.Comment: 15 pages, 5 figures, uses elsart.cl
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
Multi-core computation of transfer matrices for strip lattices in the Potts model
The transfer-matrix technique is a convenient way for studying strip lattices
in the Potts model since the compu- tational costs depend just on the periodic
part of the lattice and not on the whole. However, even when the cost is
reduced, the transfer-matrix technique is still an NP-hard problem since the
time T(|V|, |E|) needed to compute the matrix grows ex- ponentially as a
function of the graph width. In this work, we present a parallel
transfer-matrix implementation that scales performance under multi-core
architectures. The construction of the matrix is based on several repetitions
of the deletion- contraction technique, allowing parallelism suitable to
multi-core machines. Our experimental results show that the multi-core
implementation achieves speedups of 3.7X with p = 4 processors and 5.7X with p
= 8. The efficiency of the implementation lies between 60% and 95%, achieving
the best balance of speedup and efficiency at p = 4 processors for actual
multi-core architectures. The algorithm also takes advantage of the lattice
symmetry, making the transfer matrix computation to run up to 2X faster than
its non-symmetric counterpart and use up to a quarter of the original space
The lid method for exhaustive exploration of metastable states of complex systems
The `lid' algorithm performs an exhaustive exploration of neighborhoods of
local energy minima of energy landscapes. This paper describes an
implementation of the algorithm, including issues of parallel performance and
scalability. To illustrate the versatility of the approach and to stress the
common features present in landscapes of quite different systems, we present
selected results for 1) a spin glass, 2) a ferromagnet, 3) a covalent network
model for glassy systems, and 4) a polymer. The exponential nature of the local
density of states found in these systems and its relation to the ordering
transition is briefly commented upon.Comment: RevTeX, 11 pages, 1 figur
- …